Figure 3.

(a) SCF-calculated energy shift per polymer as a function of the averaged spatial discretization with attractive ($\mathsf{\Lambda }=-100$), repulsive ($\mathsf{\Lambda }=100$), and neutral ($\mathsf{\Lambda }=0$) interactions with the substrate. Here, ${\varphi }_0=2$ and $N\nu =1$. (b) SCF-calculated free energy per polymer as a function of the contour discretization. In (a,b), the empty circles correspond to uniform discretization in space (a) and contour (b), while the filled triangles correspond to their counterparts using adaptive discretization. The red horizontal line indicates zero error $\mathsf{\Delta }F=0$. The solid curves in (a,b) are fits to the function $f\left(x\right)=ax+b{x}^2+c{x}^3$. (c) Normalized segment density $\varphi \left(z\right)L/{\varphi }_0{R}_g$ as a function of $z/L$ (see text for definitions) at $\mathsf{\Lambda }=0$. The distance is rescaled by the thickness of the brush estimated by the Strong Stretching Theory (SST).